Geodesic
A Problem on Tournaments
Canadian mathematical bulletin, Tome 7 (1964) no. 3, pp. 351-356

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By a tournament we mean the outcome of a round-robin tournament in which there are no draws. Such a tournament may be represented by a graph in which the n players are represented by vertices labelled 1, 2, ..., n, and the outcomes of the games are represented by directed edges so that every pair of vertices is joined by one directed edge. We call such a graph a complete directed graph. One can also represent such a tournament by an nXn matrix T=(tij) in which tij is 1 if i beats j, and 0 otherwise, so that T is a (0, 1) matrix with tij + tji = 1 for i≠j and (by definition) tii = 0. 
Erdös, P.; Moser, L. A Problem on Tournaments. Canadian mathematical bulletin, Tome 7 (1964) no. 3, pp. 351-356. doi: 10.4153/CMB-1964-032-2
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     title = {A {Problem} on {Tournaments}},
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     doi = {10.4153/CMB-1964-032-2},
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